I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is adapted to $\mathscr{F}$, and we are currently at time $t \in [0,T)$. Let $Q$ denote the risk-neutral measure and $\beta(t) = e^{\int_0^t r(s)ds}$ be the domestic savings account/discount factor. Also, $W(t)$ is standard Brownian Motion.